Original question: How many "words" of 1 letter, 2 letters, 3 letters and 4 letters can be formed with the letters of "MAAS"
Both combinations and permutations are needed to solve this question, however I find it hard it to distinguish between the two.
I understand how to make words of 4 letters, but 1, 2 and 3 I find difficult. I can of course compute it by hand, since I only have 4 letters, but they specifically ask for permutations and combinations.
Anyone who can help me?
On
OK, let's take the case of $3$ letter words.
We can think of finding all $3$ letter words as a $2$-step process:
First, find all possible groups of $3$ letters. For example, we can decide to use both $A$'s and the single $M$
Second, now that we have decided what letters to use, we have to put them in some order to make an actual word. So, with the $3$ letters I picked before, I could make $AAM$, $AMA$, and $MAA$
The first step, where we do not care about the order of the letters, is about combinations. Think of it as creating a salad: what 'ingredients' do we want to put together? What can we combine with what?
The second step, where we do care about the order of the letters, is about permutations.
Hint : Consider the 2 $A$ letters to be distinct, what are the permutations of $MA_1A_2S$? Then, you should divide by how many times you overcount a specific word, for example $MA_1A_2S$ should be considered the same as $MA_2A_1S$.